On Orville’s ski trip, he went up with regular tires and the odometer said he drove 450 miles. He came back with snow tires on and the odometer said 440 miles. Find, to the nearest hundredth of an inch, the increase in radius of the snow tires if the radius of his regular tires was exactly 15 inches.
The wheels went around 440/450 as many times on the way back as on the way there. That means that the circumference grew to 450/440 of what it had been. 450/440 ≈ 1.0227.
So the old circumference x 1.0227 = the new. Old circumference = 15 x 2
and new circ / 2 = new radius = (15 x 2 x 1.0227)/(2) = 15 x 1.0227 = 15.3405
= new radius = (15 x 2 x 1.0227)/(2) = 15 x 1.0227 = 15.3405
So the difference in radius is about 0.34 inches (about 1/3 inch).